Problem: Rewrite as a simplified fraction. ${0.4\overline{75} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 475.7575...\\ 10x &= 4.7575...\end{align*}}$ Subtracting the two equations, we have: ${990x = 471}$ ${x = \dfrac{471}{990}} $ ${x = \dfrac{157}{330}} $